“The workmanship is indeed very beautiful,” answered Archimedes, “but—but the gold—”
“The gold is all there,” cried the king.“I weighed it on my own scales.”
“True,” said Archimedes,“but it does not appear to have the same rich red color that it had in the lump. It is not red at all, but a brilliant yellow, as you can plainly see.”
“Most gold is yellow,” said Hiero，“but now that you speak of it I do remember that when this was in the lump it had a much richer color.”
“What if the goldsmith has kept out a pound or two of the gold and made up the weight by adding brass or silver?” asked Archimedes.
“Oh, he could not do that,” said Hiero. “The gold has merely changed its color in the working.”
But the more he thought of the matter the less pleased he was with the crown. At last he said to Archimedes, “Is there any way to find out whether that goldsmith really cheated me, or whether he honestly gave me back my gold?”
“I know of no way,” was the answer.
But Archimedes was not the man to say that anything was impossible. He took great delight in working out hard problems, and when any question puzzled him he would keep studying until he found some sort of answer to it. And so, day after day, he thought about the gold and tried to find some way by which it could be tested without doing harm to the crown.